Challenges in Stochastic Binary Systems

Stochastic Binary Systems (SBS) are mathematical models of multi-component on-off systems subject to random failures on its components. In this abstract setting, an SBS can model a network, an information system or the operation of an industrial automatic process, among many others. Given the importance of its applications, recent works from the literature aim to understand the system reliability and combinatorics of some distinguished sub-classes of SBS. In this paper we revisit the progress in this field. The most challenging problems in the analysis and practice of SBS are also discussed.

[1]  H. Cramér.  Half a Century with Probability Theory: Some Personal Recollections , 1976 .

[2]  Douglas H. Wiedemann,et al.  A computation of the eighth Dedekind number , 1991 .

[3]  Nimrod Megiddo,et al.  On the complexity of polyhedral separability , 1988, Discret. Comput. Geom..

[4]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[5]  R. P. Dilworth,et al.  A DECOMPOSITION THEOREM FOR PARTIALLY ORDERED SETS , 1950 .

[6]  Pablo Romero,et al.  Duality in stochastic binary systems , 2016, 2016 8th International Workshop on Resilient Networks Design and Modeling (RNDM).

[7]  Gerardo Rubino,et al.  Rare Event Simulation using Monte Carlo Methods , 2009 .

[8]  J. Scott Provan,et al.  The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected , 1983, SIAM J. Comput..

[9]  Charles E. Clark,et al.  Monte Carlo , 2006 .

[10]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[11]  Anthony Widjaja,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2003, IEEE Transactions on Neural Networks.

[12]  Pablo Romero,et al.  Reliability maximization in stochastic binary systems , 2018, 2018 21st Conference on Innovation in Clouds, Internet and Networks and Workshops (ICIN).

[13]  David K. Smith.  Theory of Linear and Integer Programming , 1987 .

[14]  Awelani Malada,et al.  Stochastic reliability modelling for complex systems , 2007 .

[15]  Philip F. Reichmeider.  The Equivalence of Some Combinatorial Matching Theorems , 1984 .

[16]  Ronald J. Gould.  Recent Advances on the Hamiltonian Problem: Survey III , 2014, Graphs Comb..

[17]  Pablo Romero,et al.  Building Reliability Bounds in Stochastic Binary Systems , 2018, 2018 10th International Workshop on Resilient Networks Design and Modeling (RNDM).

[18]  Herbert Edelsbrunner,et al.  Minimum Polygonal Separation , 1986, Inf. Comput..

[19]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[20]  Michael O. Ball,et al.  Computational Complexity of Network Reliability Analysis: An Overview , 1986, IEEE Transactions on Reliability.

[21]  A. Rosenthal.  Computing the Reliability of Complex Networks , 1977 .

[22]  Michael O. Ball,et al.  Complexity of network reliability computations , 1980, Networks.

[23]  Charles J. Colbourn,et al.  The Combinatorics of Network Reliability , 1987 .

[24]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[25]  Vadim V. Lozin,et al.  Words and Graphs , 2016, Monographs in Theoretical Computer Science. An EATCS Series.

[26]  I. Olkin,et al.  A Multivariate Exponential Distribution , 1967 .

[27]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .